# Product rule for differentiation

From Calculus

## Statement for two functions

### Verbal statement

If two (possibly equal) functions are differentiable at a given real number, then their pointwise product is also differentiable at that number and the derivative of the product is the sum of two terms: the derivative of the first function times the second function and the first function times the derivative of the second function.

### Statement with symbols

Suppose and are functions, both of which are differentiable at a real number . Then, the product function , defined as is also differentiable at , and the derivative at is given as follows:

or equivalently:

If we consider the general expressions rather than evaluation at a particular point , we can rewrite the above as:

or equivalently: